Growth of Selmer Groups over function fields

Aftab Pande

Growth of Selmer Groups over function fields

Number Theory 2013-12-02 v3

Authors: Aftab Pande

Abstract

We study the rank of the $p$ -Selmer group $Sel_p(A/k)$ of an abelian variety $A/k$ , where $k$ is a function field. If $K/k$ is a quadratic extension and $F/k$ is a dihedral extension and the $\mathbb{Z}_p$ -corank of $Sel_p (A/K)$ is odd, we show that the $\mathbb{Z}_p$ -corank of $Sel_p(A/F) \geq [F:K]$ . The result uses the theory of local constants developed by Mazur-Rubin for elliptic curves over number fields.

Keywords

elliptic curves field theory

Cite

@article{arxiv.1106.3287,
  title  = {Growth of Selmer Groups over function fields},
  author = {Aftab Pande},
  journal= {arXiv preprint arXiv:1106.3287},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author due to a mistaken assumption about local Tate duality

Growth of Selmer Groups over function fields

Abstract

Keywords

Cite

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